Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Textbook Question
Chapter 4.1, Problem 10ES
Use the formulas given in this section to determine, as accurately as possible, approximations for each missing entry in the following tables.
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Chapter 4 Solutions
Numerical Analysis
Ch. 4.1 - Use the forward-difference formulas and...Ch. 4.1 - The data in Exercise 1 were taken from the...Ch. 4.1 - Use the most accurate three-point formula to...Ch. 4.1 - Use the most accurate three-point formula to...Ch. 4.1 - The data in Exercise 5 were taken from the...Ch. 4.1 - The data in Exercise 6 were taken from the...Ch. 4.1 - Prob. 9ESCh. 4.1 - Use the formulas given in this section to...Ch. 4.1 - The data in Exercise 9 were taken from the...Ch. 4.1 - Prob. 12ES
Ch. 4.1 - Use the following data and the knowledge that the...Ch. 4.1 - Prob. 14ESCh. 4.1 - Prob. 15ESCh. 4.1 - Prob. 16ESCh. 4.1 - Prob. 17ESCh. 4.1 - Prob. 18ESCh. 4.1 - Prob. 19ESCh. 4.1 - Prob. 20ESCh. 4.1 - Prob. 21ESCh. 4.1 - In a circuit with impressed voltage (t) and...Ch. 4.1 - In Exercise 9 of Section 3.4, data were given...Ch. 4.1 - Derive an O(h4) five-point formula to approximate...Ch. 4.1 - Use the formula derived in Exercise 24 and the...Ch. 4.1 - a. Analyze the round-off errors, as in Example 4,...Ch. 4.1 - Derive a method for approximating f (x0) whose...Ch. 4.1 - Consider the function e(h)=h+h26M, where M is a...Ch. 4.1 - Prob. 1DQCh. 4.1 - Prob. 2DQCh. 4.2 - Apply the extrapolation process described in...Ch. 4.2 - Add another line to the extrapolation table in...Ch. 4.2 - The following data give approximations to the...Ch. 4.2 - Prob. 6ESCh. 4.2 - Prob. 7ESCh. 4.2 - The forward-difference formula can be expressed as...Ch. 4.2 - Prob. 9ESCh. 4.2 - Prob. 10ESCh. 4.2 - Prob. 11ESCh. 4.2 - Prob. 12ESCh. 4.2 - Prob. 13ESCh. 4.3 - Approximate the following integrals using the...Ch. 4.3 - Approximate the following integrals using the...Ch. 4.3 - Find a bound for the error in Exercise 1 using the...Ch. 4.3 - Prob. 4ESCh. 4.3 - Repeat Exercise 1 using Simpsons rule. 1....Ch. 4.3 - Prob. 6ESCh. 4.3 - Prob. 7ESCh. 4.3 - Prob. 8ESCh. 4.3 - Prob. 9ESCh. 4.3 - Prob. 10ESCh. 4.3 - Prob. 11ESCh. 4.3 - Prob. 12ESCh. 4.3 - The Trapezoidal rule applied to 02f(x)dx gives the...Ch. 4.3 - Prob. 14ESCh. 4.3 - Approximate the following integrals using formulas...Ch. 4.3 - Prob. 17ESCh. 4.3 - Suppose that the data of Exercise 17 have...Ch. 4.3 - Prob. 19ESCh. 4.3 - Prob. 20ESCh. 4.3 - The quadrature formula...Ch. 4.3 - The quadrature formula...Ch. 4.3 - Find the constants c0, c1, and x1 so that the...Ch. 4.3 - Find the constants x0, x1, and c1 so that the...Ch. 4.3 - Prob. 25ESCh. 4.3 - Prob. 26ESCh. 4.3 - Prob. 27ESCh. 4.3 - Derive Simpsons Three-Eighths rule (the closed...Ch. 4.3 - Prob. 1DQCh. 4.3 - Prob. 2DQCh. 4.4 - Use the Composite Trapezoidal rule with the...Ch. 4.4 - Prob. 2ESCh. 4.4 - Use the Composite Simpsons rule to approximate the...Ch. 4.4 - Prob. 4ESCh. 4.4 - Prob. 5ESCh. 4.4 - Prob. 6ESCh. 4.4 - Prob. 7ESCh. 4.4 - Prob. 8ESCh. 4.4 - Prob. 9ESCh. 4.4 - Prob. 10ESCh. 4.4 - Determine the values of n and h required to...Ch. 4.4 - Repeat Exercise 11 for the integral 0x2cosxdx. 11....Ch. 4.4 - Determine the values of n and h required to...Ch. 4.4 - Repeat Exercise 13 for the integral 12xlnxdx. 13....Ch. 4.4 - Prob. 15ESCh. 4.4 - Prob. 17ESCh. 4.4 - A car laps a race track in 84 seconds. The speed...Ch. 4.4 - Prob. 19ESCh. 4.4 - Prob. 20ESCh. 4.4 - Prob. 21ESCh. 4.4 - Prob. 23ESCh. 4.4 - Prob. 24ESCh. 4.4 - Prob. 25ESCh. 4.4 - Prob. 26ESCh. 4.4 - Prob. 1DQCh. 4.4 - Prob. 2DQCh. 4.5 - Use Romberg integration to compute R3, 3 for the...Ch. 4.5 - Use Romberg integration to compute R3, 3 for the...Ch. 4.5 - Prob. 3ESCh. 4.5 - Prob. 4ESCh. 4.5 - Use the following data to approximate 15f(x)dx as...Ch. 4.5 - Prob. 9ESCh. 4.5 - Prob. 10ESCh. 4.5 - Prob. 11ESCh. 4.5 - Romberg integration for approximating 01f(x)dx...Ch. 4.5 - Prob. 15ESCh. 4.5 - Prob. 18ESCh. 4.5 - Prob. 19ESCh. 4.5 - Prob. 1DQCh. 4.5 - Prob. 4DQCh. 4.6 - Prob. 1ESCh. 4.6 - Prob. 2ESCh. 4.6 - Prob. 11ESCh. 4.6 - Prob. 12ESCh. 4.6 - Could Romberg integration replace Simpsons rule in...Ch. 4.7 - Approximate the following integrals using Gaussian...Ch. 4.7 - Approximate the following integrals using Gaussian...Ch. 4.7 - Repeat Exercise 1 with n = 3. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 3. 2. Approximate the...Ch. 4.7 - Repeat Exercise 1 with n = 4. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 4. 2. Approximate the...Ch. 4.7 - Repeat Exercise 1 with n = 5. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 5. 2. Approximate the...Ch. 4.7 - Describe the differences and similarities between...Ch. 4.7 - Prob. 2DQCh. 4.8 - Prob. 1DQCh. 4.8 - Prob. 2DQCh. 4.8 - Prob. 3DQCh. 4.8 - Prob. 4DQCh. 4.9 - Suppose a body of mass m is traveling vertically...Ch. 4.9 - The Laguerre polynomials {L0(x), L1(x) ...} form...Ch. 4.9 - Prob. 7ESCh. 4.9 - Prob. 8ESCh. 4.9 - Prob. 9ESCh. 4.9 - Prob. 1DQCh. 4.9 - Prob. 2DQ
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- Using Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates). HINT: Pay closeattention to both the 1’s and the 0’s of the function.arrow_forwardRecall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n (=15) is the product of the two prime numbers 3 and 5.1. Find an encryption key e for for the pair (e, n)2. Find a decryption key d for for the pair (d, n)3. Given the plaintext message x = 3, find the ciphertext y = x^(e) (where x^e is the message x encoded with encryption key e)4. Given the ciphertext message y (which you found in previous part), Show that the original message x = 3 can be recovered using (d, n)arrow_forwardTheorem 1: A number n ∈ N is divisible by 3 if and only if when n is writtenin base 10 the sum of its digits is divisible by 3. As an example, 132 is divisible by 3 and 1 + 3 + 2 is divisible by 3.1. Prove Theorem 1 2. Using Theorem 1 construct an NFA over the alphabet Σ = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}which recognizes the language {w ∈ Σ^(∗)| w = 3k, k ∈ N}.arrow_forward
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